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Simplifying 18d2 + -84d + 96 = 0 Reorder the terms: 96 + -84d + 18d2 = 0 Solving 96 + -84d + 18d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '6'. 6(16 + -14d + 3d2) = 0 Factor a trinomial. 6((2 + -1d)(8 + -3d)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + -1d)' equal to zero and attempt to solve: Simplifying 2 + -1d = 0 Solving 2 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1d = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1d = 0 + -2 -1d = 0 + -2 Combine like terms: 0 + -2 = -2 -1d = -2 Divide each side by '-1'. d = 2 Simplifying d = 2Subproblem 2
Set the factor '(8 + -3d)' equal to zero and attempt to solve: Simplifying 8 + -3d = 0 Solving 8 + -3d = 0 Move all terms containing d to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3d = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3d = 0 + -8 -3d = 0 + -8 Combine like terms: 0 + -8 = -8 -3d = -8 Divide each side by '-3'. d = 2.666666667 Simplifying d = 2.666666667Solution
d = {2, 2.666666667}
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